This is a two-year cooperative research project between Professor Michael G. Akritas, Department of Statistics, The Pennsylvania State University, and Professor Willem Albers, Department of Medical Informatics and Statistics, University of Limburg, The Netherlands. The mathematicians are cooperating in a study of tests and estimators that are based on distance measures, the associated use of the bootstrap technique, and the application of the bootstrap to certain rank procedures including multiple comparisons. The work may lead to the development of a common theory for testing and estimation with both censored and uncensored data, and so is relevant to data arising from reliability, life testing, and medical studies. Some of the performance aspects that will be considered are: sensitivity to tail alternatives and to crossing hazards alternatives for the one- and two- sample problem, respectively, and robustness of the estimators and how this depends on the degree of censoring. The second aspect of the work is concerned with applications of the bootstrap technique to approximating the null distribution or the null variance of some common rank statistics with or without censoring, and to rank-based multiple comparison procedures with both censored and uncensored data. This study is concerned with developing and refining statistical procedures for making "goodness of fit" tests that permit one to judge how well a chosen model fits data derived from experimental observations. In particular, applications of the procedures will be made to situations in which data are "censored," that is, missing for some reason, as when a patient drops out of a clinical study before the study is over. The methods would permit a comparison of the effectiveness of two or more treatments for a disease, for example, as well as indicate the levels of confidence that should be placed on the conclusions that are drawn. The so-called "bootstrap" technique, a relatively new and powerful statistical tool, will be applied in this study to obtain approximations to the true probability distribution of parameters of interest. Professor Akritas has considerable experience in applying statistical methods to censored data. Professor Albers is a recognized authority in asymptotic theory with special emphasis in nonparametric methods. Collaboration by the two researchers on the many mathematical and computational aspects of this work should greatly facilitate the development of the new procedures as well as their comparison with existing statistical methods.
